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Le Playbook

Kurtosis

2 articles
Probability & StatisticsLicenceAnalyse13 min

A Coin Flip Between Two Volatilities Is Enough to Make a Smile

Let a fair coin decide at the start of the year whether the share runs at 15 or 35 percent, price calls in that world, then read the volatilities back out with the constant-volatility formula: 28.43, 25.91, 24.97, 25.68 and 27.16 percent across five strikes. The floor sits at the money and below the 25 percent average of the two regimes, which one second derivative settles without any numerics. The usual explanation for the wings is refuted here, because the coin-flip world is less likely to clear 130 than a flat 25 percent and its option is still worth 27 percent more.

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Probability & StatisticsLicenceExplication12 min

A Shock Is Still Half Remembered Thirty-Four Days Later

Two weights that add to 0.98 give the variance forecast a half-life of 34.31 days; delete the second one and the half-life is 0.2744 days, gone before the next open. The same recursion turns strictly normal daily draws into a year with kurtosis exactly 297/67, and one shuffle of those same numbers separates the fat tail from the clustering. It also has a condition nobody quotes: stationarity is not enough for that kurtosis to be finite.

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